Go to Appearance > Editor and edit ‘loop.php‘.
Just under
/* Start the Loop.
*
* In Twenty Ten we use the same loop in multiple contexts.
* It is broken into three main parts: when we're displaying
* posts that are in the gallery category, when we're displaying
* posts in the asides category, and finally all other posts.
*
* Additionally, we sometimes check for whether we are on an
* archive page, a search page, etc., allowing for small differences
* in the loop on each template without actually duplicating
* the rest of the loop that is shared.
*
* Without further ado, the loop:
*/ ?>
replace following bit of code
<?php while ( have_posts() ) : the_post(); ?>
with
<?php if ( is_home() ) { query_posts($query_string . '&cat=-5'); } ?>
Notice the ‘=-5‘ this tells the homepage not to display posts from the post category id ’5′.
If you want to stop more than one category from being displayed just separate with a comma and write ,-# , where # is the id number of the category – see below.
<?php if ( is_home() ) { query_posts($query_string . '&cat=-5,-3'); } ?>
To revert back to showing posts from all categories just change it back to
<?php if ( is_home() ) { query_posts($query_string . '&cat'); } ?>